Residual stiffness analysis of flexural concrete elements with composite reinforcement

Abstract

Various materials and reinforcement technologies have been created, but this versatility causes a severe engineering problem – there is no versatile technique suitable for the development of efficient reinforcement system. In reinforced concrete systems, residual stiffness of the element can estimate the efficiency of the reinforcement. The stiffness is closely related to the structural integrity of cracked sections resisting the deformation increase of the member. This study introduces a simplified ap-proach for the flexural stiffness analysis. It employs a new testing layout designed with the purpose to form multiple cracks in a small laboratory specimen. The proposed analytical model is based on the following assumptions: smeared crack concept; linear strain distribution within the section depth; elastic behaviour of reinforcement and compressive concrete; a rectangular distribution of stresses in the tensile concrete. The latter assumption enables obtaining a closed-form solution of the residual stiffness problem in terms of the equivalent tensile stresses in the concrete. The achieved solution requires neither iterative calculations nor a description of the loading history. The proposed methodol-ogy is also acceptable for estimating residual stiffness of elements with various combinations of rein-forcement. The application of the proposed technique is illustrated experimentally. Several composite reinforcement schemes, including internal steel and glass fibre reinforced polymer (GFRP) bars, carbon fibre reinforced polymer (CFRP) sheets and near-surface mounted (NSM) strips in different combinations, are considered. The analysis of the test results reveals a substantiate efficiency of the external CFRP reinforcement systems concerning the internal reinforcement as the reference. The application of the CFRP sheets substantially increases the effectiveness of the tensile concrete. In essence, the decay of the equivalent stresses acting to the tensile concrete does not exceed 50% of the tensile strength of the concrete in the presence of the external reinforcement. However, the formation of a critical shear crack caused the failure of all specimens with composite reinforcement. That is a consequence of low resistance of the fibre reinforced polymer materials to a shear load.